Sorry for the inconvenience, that's an issue that will be fixed in an upcoming release of Map Tour.
Looks like your basemap was in a different projection than web mercator.
When you switched to your basemap in ArcGIS.com viewer, your points got reprojected, but when you got back to Imagery basemap with the Map Tour builder, your points didn't get reprojected to web mercartor.
Your data are still there and looks valid, just that they can't be displayed because they are not in the expected projection.
To fix that, with ArcGIS.com viewer if switch the basemap to yours then save the webmap and then switch back to Imagery basemap, your Map Tour points should be reprojected to web mercator and your story usable again.